Advanced Engineering Economy Contemporary Engineering Economics, 5th edition, © 2010

Chapter Opening Story How Much Will It Cost to Send Your Child to College in Year 2015?  A year in college cost $17,800 in  Due to inflation, the college expense has been increasing at a rate of 6.5% annually.  Then, in 2015 a year in college would cost about $33,413. Contemporary Engineering Economics, 5th edition, © 2010 College Cost Calculator

Inflation and Economic Analysis  What is inflation?  How do we measure inflation?  How do we incorporate the effect of inflation in equivalence calculation? Contemporary Engineering Economics, 5th edition, © 2010

What is Inflation? Definition: Inflation is the rate at which the general level of prices and goods and services is rising, and subsequently, purchasing power is falling. Time Value of Money Contemporary Engineering Economics, 5th edition, © 2010  Earning Power  Purchasing Power  Earning Power  Investment Opportunity  Purchasing Power  Decrease in purchasing power (inflation)  Increase in purchasing power (deflation)

Inflation - Decrease in Purchasing Power Contemporary Engineering Economics, 5th edition, © $ $100 You could buy 50 Big Macs in year 1990 with $100 You can only buy 28.5 Big Macs in year $2.00 / unit $3.50 / unit 75% Price change due to inflation The $100 in year 2010 has only $57 worth purchasing power of 1990

Deflation - Increase in Purchasing Power Contemporary Engineering Economics, 5th edition, © $ $100 You could purchase gallons of purified drink water a year ago. You can now purchase 80 gallons of purified drink water. $1.57 / gallon$1.25 / gallon Price change due to deflation 20.38%

Inflation Terminology - I Producer Price Index: a statistical measure of industrial price change, compiled monthly by the Bureau of Labor Statistics, U.S. Department of Labor Consumer Price Index: a statistical measure of change, over time, of the prices of goods and services in major expenditure groups—such as food, housing, apparel, transportation, and medical care—typically purchased by urban consumers Average Inflation Rate (f): a single average rate that accounts for the effect of varying yearly inflation rates over a period of several years. General Inflation Rate (f ): the average inflation rate calculated based on the CPI for all items in the market basket. Contemporary Engineering Economics, 5th edition, © 2010

Consumer Price Index Consumer Price Index (CPI): the CPI compares the cost of a sample “market basket” of goods and services in a specific period relative to the cost of the same “market basket” in an earlier reference period. This reference period is designated as the base period. CPI (Old measure) – Base Period = (January) CPI (New measure) – Base Period ( ) (January) Contemporary Engineering Economics, 5th edition, © 2010

Selected Price Indexes (Index for Base Year = 100, Calendar Month = April) Contemporary Engineering Economics, 5th edition, © 2010

Average Inflation Rate (f ) Fact:  Base Price = $100 (year 0)  Inflation rate (year 1) = 4%  Inflation rate (year 2) = 8% Find: Average inflation rate over 2 years? Step 1: Find the actual inflated price at the end of year 2. $100 ( ) ( ) = $ Step 2: Find the average inflation rate by solving the following equivalence equation. $100 ( 1+ f) 2 = $ f = 5.98% Contemporary Engineering Economics, 5th edition, © 2010 $100 $

Example: Average Inflation Rate Sample Calculation for Average Inflation rate for Gasoline: Given: P = 127.3, F = 175.3, N = = 9. Find: f Average Inflation Rate Contemporary Engineering Economics, 5th edition, © 2010

General Inflation Rate (f) Formula: Calculation: Given: CPI for 2009 = 213.2, CPI for 2000 = Find: f Contemporary Engineering Economics, 5th edition, © 2010

Example Yearly and Average Inflation Rates  Year cost data:  Find: Yearly and Average inflation rates Solution: Contemporary Engineering Economics, 5th edition, © 2010 YearCost 0$504, , , ,500

Actual Dollars (A n ): Estimates of future cash flows for year n that take into account any anticipated future changes in amount caused by inflationary or deflationary effects. Constant Dollars (A n ’ ): Estimates of future cash flows for year n in constant purchasing power, independent of the passage of time (or base period). Contemporary Engineering Economics, 5th edition, © 2010 Inflation Terminology – II

Finding Actual Dollars Conversion from Constant to Actual Dollars General inflation rate = 5% Contemporary Engineering Economics, 5th edition, © 2010

Finding Constant Dollars Conversion from Actual to Constant dollars Contemporary Engineering Economics, 5th edition, © 2010 Example General inflation rate of 5%

Equivalence Calculations under Inflation Contemporary Engineering Economics, 5th edition, © 2010 Types of Analysis Method Constant-Dollar AnalysisActual-Dollar Analysis Types of Cash Flows Estimated in Constant DollarsEstimated in Actual Dollars Types of Interest Rate Market Interest Rate (i)Inflation-free Interest Rate (i’)

Inflation Terminology - III Inflation-free interest rate (i’): an estimate of the true earning power of money when the inflation effects have been removed (also known as real interest rate). Market interest rate (i): an interest rate which takes into account the combined effects of the earning value of capital and any anticipated changes in purchasing power (also known as inflation-adjusted interest rate). Contemporary Engineering Economics, 5th edition, © 2010

Inflation and Cash Flow Analysis Contemporary Engineering Economics, 5th edition, © 2010  Constant Dollar analysis  Estimate all future cash flows in constant dollars.  Use i’ as an interest rate to find the equivalent worth.  Actual Dollar Analysis  Estimate all future cash flows in actual dollars.  Use i as an interest rate to find the equivalent worth.

When do we Prefer Constant Dollar Analysis? In the absence of inflation, all economic analyses up to this point is, in fact, the constant dollar analysis. Constant dollar analysis is common in the evaluation of many long-term public projects, because governments do not pay income taxes. For private sector, income taxes are imposed based on the taxable income in actual dollars, so the actual dollar analysis is more common. Contemporary Engineering Economics, 5th edition, © 2010

Two Alternate Ways in Conducting Actual Dollars Analysis Contemporary Engineering Economics, 5th edition, © 2010 Method 1: Deflation Method - Step 1:Bring all cash flows to have common purchasing power. - Step 2:Consider the earning power. Method 2: Adjusted-discount Method - Combine Steps 1 and 2 into one step.

Example: Deflation Method Step 1: Converting Actual Dollars into Constant Dollars Step 2: Calculating Equivalent Present Worth Contemporary Engineering Economics, 5th edition, © 2010

Graphical Overview on Deflation Method (Example): Converting actual dollars to constant dollars and then to equivalent present worth Contemporary Engineering Economics, 5th edition, © $75,000$30,476 $32,381 $28,334$23,858 $45,455 -$75,000 $32,000 $35,700 $32,800 $29,000 $58,000 -$75,000 $27,706 $26,761 $21,288 $16,295 $28,218 $45,268 Actual Dollars Constant Dollars Present Worth n = 0 n = 1n = 2n = 3n = 4n = 5

Adjusted-Discount Method – Perform Deflation and Discounting in One Step Contemporary Engineering Economics, 5th edition, © 2010 Step 1 Step 2 o Discrete Compounding o Continuous Compounding

Example: Adjusted-Discounted Method Given: inflation-free interest rate = 0.10, general inflation rate = 5%, and cash flows in actual dollars Find: i and NPW Contemporary Engineering Economics, 5th edition, © 2010

Graphical Overview on Adjusted Discount Method: Converting actual dollars to present worth dollars by applying the market interest rate Contemporary Engineering Economics, 5th edition, © 2010 n = 0 n = 1n = 2n = 3n = 4n = 5 -$75,000 $32,000 $35,700 $32,800 $29,000 $58,000 Actual Dollars -$75,000 $27,706 $26,761 $21,288 $16,295 $28,218 $45,268 Present Worth

Contemporary Engineering Economics, 5th edition, © 2010 Mixed-Dollar Analysis – College Savings Plan - Equivalence Calculation with Composite Cash Flow Elements Age (Current Age = 5 Years Old) Estimated College Expenses in Today’s Dollars College Expenses Converted into Equivalent Actual Dollars 18 (Freshman)$30,000$30,000(F/P,6%,13) = $63, (Sophomore)30,00030,000(F/P,6%,14) = 67, (Junior)30,00030,000(F/P,6%,15) = 71, (senior)30,00030,000(F/P,6%,16) = 76,211 Approach: Convert any cash flow elements in constant dollars into actual dollars. Then use the market interest rate to find the equivalent present value. Assume f = 6% and i = 8% compounded quarterly.

Solution: Required Quarterly Contributions to College Funds Contemporary Engineering Economics, 5th edition, © 2010 V 1 = C(F/A, 2%, 48) V 2 = $229,211 Let V 1 = V 2 and solve for C: C = $2,888.48

Effects of Inflation on Projects with Depreciable Assets Contemporary Engineering Economics, 5th edition, © 2010 ItemEffects of Inflation Depreciation expense Salvage value Depreciation expense is charged to taxable income in dollars of declining values; taxable income is overstated, resulting in higher taxes Inflated salvage value combined with book values based on historical costs results in higher taxable gains. Note: Depreciation expenses are based on historical costs and always expressed in actual dollars

Example 11.8 Reconsider the Automated Machining Center project discussed earlier. What will happen to this investment project if  the general inflation during the next five years is expected to increase by 5% annually,  sales, operating costs, and working capital requirements are assumed to increase accordingly,  depreciation will remain unchanged, but taxes, profits, and thus cash flow will be higher.  the firm’s inflation-free interest rate is known to be 15%. Determine the PW of the project. Contemporary Engineering Economics, 5th edition, © 2010

Solution: Excel Worksheet Contemporary Engineering Economics, 5th edition, © 2010

Effects of Inflation on Return on Investment Contemporary Engineering Economics, 5th edition, © 2010 ItemEffects of Inflation Rate of Return and NPW Unless revenues are sufficiently increased to keep pace with inflation, tax effects and/or a working capital drain result in lower rate of return or lower NPW.

Example IRR Analysis with Inflation  IRR in the absence of inflation  IRR Calculation under Inflation Contemporary Engineering Economics, 5th edition, © 2010

Rate of Return Analysis under Inflation Principle: True (real) rate of return should be based on constant dollars. If the rate of return is computed based on cash flows in actual dollars, the real rate of return can be calculated as: Contemporary Engineering Economics, 5th edition, © 2010 n Net cash flows in actual dollars Net cash flows in constant dollars $30,000 13,570 15,860 13,358 13,626 -$30,000 12,336 13,108 10,036 9,307 IRR 31.34% 19.40%

Decision Criterion If you use 31.34% as your IRR, you should use a market interest rate (or inflation-adjusted MARR) to make an accept and reject decision. If you use 19.40% as your IRR, you should use an inflation-free interest rate (inflation-free MARR) to make an accept and reject decision. In our example, MARR’ = 20%. Contemporary Engineering Economics, 5th edition, © 2010

Effects of Inflation on Working Capital Contemporary Engineering Economics, 5th edition, © 2010 ItemEffects of Inflation Working capital requirement Known as working capital drain, the cost of working capital increases in an inflationary environment.

Example Effects of Inflation on Working Capital Contemporary Engineering Economics, 5th edition, © 2010

Summary The Consumer Price Index (CPI) is a statistical measure of change, over time, of the prices of goods and services in major expenditure groups—such as food, housing, apparel, transportation, and medical care—typically purchased by urban consumers. Inflation is the term used to describe a decline in purchasing power evidenced in an economic environment of rising prices. Deflation is the opposite: An increase in purchasing power evidenced by falling prices. Contemporary Engineering Economics, 5th edition, © 2010

The general inflation rate (f) is an average inflation rate based on the CPI. An annual general inflation rate ( ) can be calculated using the following equation: Specific, individual commodities do not always reflect the general inflation rate in their price changes. We can calculate an average inflation rate for a specific commodity (j) if we have an index (that is, a record of historical costs) for that commodity. Contemporary Engineering Economics, 5th edition, © 2010

Project cash flows may be stated in one of two forms  Actual dollars (A n ): Dollars that reflect the inflation or deflation in the economy.  Constant dollars (A’ n ): Dollars in Year 0 purchasing dollars. Interest rates for project evaluation may be stated in one of two forms:  Market interest rate (i): A rate which combines the effects of interest and inflation; used with actual dollar analysis.  Inflation-free interest rate (i’): A rate from which the effects of inflation have been removed; this rate is used with constant dollar analysis. Contemporary Engineering Economics, 5th edition, © 2010

To calculate the present worth of cash flows in actual dollars, we can use a two-step or a one-step process:  Deflation method—two steps: 1. Convert cash flows in actual dollars by deflating with the general inflation rate of 2. Calculate the PW of cash flows in constant dollars by discounting at i’  Adjusted-discount method—one step 1. Compute the market interest rate. 2. Use the market interest rate directly to find the present value of cash flows in actual dollars. Contemporary Engineering Economics, 5th edition, © 2010